The historical rates of return on the emerging market mutual fund for the last five years are 10%, 6%, 23%, -15%, and 11%. Vincent's marginal tax rate on invest- ment is 30%. Since he traded frequently, he had to pay taxes on the mutual fund every year. The rate of inflation was 3% per year. Calculate the following:

1. geometric mean after-tax rate of return

2. geometric mean after-tax real rate of return